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new fatou.gp program - Printable Version

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RE: new fatou.gp program - JmsNxn - 07/07/2022

Hmm, Okay

That's something I've never seen before. You are right, Catullus, I've made a mistake somewhere in my observations.

From here, I don't have an answer to your question. I am not familiar enough with the fatou.gp program. I thought it'd run the Schroder for \(i\), didn't realize it ran the kneser algorithm.

I guess the best statement that I have is that for \(1 < b < \eta\) Sheldon's algorithm runs a kneser algorithm which roughly approximates the Schroder iteration. But for complex values it runs the Kneser iteration, as an analytic continuation. I'm still wary though of this solution.

I apologize, my mistake.


RE: new fatou.gp program - Catullus - 07/09/2022

Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision?
How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey?


RE: new fatou.gp program - JmsNxn - 07/10/2022

(07/09/2022, 06:55 AM)Catullus Wrote: Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision?
How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey?

You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise.


RE: new fatou.gp program - Catullus - 07/10/2022

(07/10/2022, 01:51 AM)JmsNxn Wrote:
(07/09/2022, 06:55 AM)Catullus Wrote: Then what was up with the spikes in the imaginary part with one precision, and then straight line at zero at a higher precision?
How do I use fatou.gp to show the non real valuedness of the analytic continuation of the Kneser method, with base the pith root of pi in a way that is not spikey?

You never use numerical approximation as a proof of anything. So, you can't. But the spikes are just noise in the program... nothing you can do about that--except write your own program that tries to reduce noise.
What about using tetcomplex.gp?